The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation is 45°. Find the height of tower PQ and the distance XQ.
Heights & Distances
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Question

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation is 45°. Find the height of tower PQ and the distance XQ.

Heights & Distances

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KnowledgeBoat · Accepted Answer

Given, XY = 40 m ⇒ PQ = h (let) ⇒ ∠PXQ = 60° and ∠RYQ = 45° ⇒ RP = XY = 40 m and RQ = PQ - RP = h - 40 In △RYQ, From figure, PX = RY = h - 40 In △PXQ, In △QPX, Hence, height of tower PQ is 94.64 and XQ = 109.28 m.

Mathematics

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation is 45°. Find the height of tower PQ and the distance XQ.

Heights & Distances

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